- Lewis played a game of space invaders. He scored points for each spaceship that he captured.
Lewis scored 140 points for capturing his first spaceship.
He scored 160 points for capturing his second spaceship, 180 points for capturing his third spaceship, and so on.
The number of points scored for capturing each successive spaceship formed an arithmetic sequence.
- Find the number of points that Lewis scored for capturing his 20th spaceship.
- Find the total number of points Lewis scored for capturing his first 20 spaceships.
Sian played an adventure game. She scored points for each dragon that she captured. The number of points that Sian scored for capturing each successive dragon formed an arithmetic sequence.
Sian captured \(n\) dragons and the total number of points that she scored for capturing all \(n\) dragons was 8500 .
Given that Sian scored 300 points for capturing her first dragon and then 700 points for capturing her \(n\)th dragon,
- find the value of \(n\).